Duality in Field Theories

In Electromagnetic Theory [> s.a. electromagnetism.]
* Idea: The transformations of the quantities {(_e, _m), (j_e, j_m), (E, H), (D, B)}, defined by

x_e = x_e' cos + x_m' sin ,      x_m = –x_e' sin + x_m' cos .

* Properties: The values of E × H, E · D + B · H, T_ab, and the Maxwell equations, are left invariant.
* Applications: Duality between the Aharonov-Bohm and Aharonov-Casher effects.
@ General references: Misner & Wheeler AP(57); Montonen & Olive PLB(77) [monopole]; Zhu JPA(89) [complexions]; Anandan gq/95 [topological phases]; Witten SelMath(95)ht [on a general manifold]; Deser & Sarioglu PLB(98)ht/97 [and Lorentz invariance]; Igarashi et al NPB(98)ht; Hatsuda et al NPB(99)ht [invariant lagrangians]; Li & Naón MPLA(01)ht/00; Przeszowski JPA(05)ht [light-front variables]; Julia ht/05-in [generalization].
@ In quantum electrodynamics: Buhmann & Scheel a0806 [macroscopic].
@ In non-linear electrodynamics: Gibbons & Rasheed NPB(95)ht; Gaillard & Zumino ht/97, ht/97 [non-linear].
@ From Lagrangian: Bhattacharyya & Gangopadhyay MPLA(00)ht/98.

In Other Theories > s.a. hamiltonian systems; higher-order lagrangians; lagrangian dynamics; M-theory; strings.
> In quantum mechanics: What Isidro calls duality is in reality an ambiguity in the choice of complex structure used in quantizing a classical theory.
@ General references: Savit RMP(80); Banerjee & Ghosh JPA(98) [chiral oscillator model]; Olive ht/02-in.
@ In quantum mechanics: Isidro MPLA(03)qp, PLA(03)qp, qp/03-in [projective phase space], MPLA(04)qp/03 [torus phase space]; > s.a. coherent states.
@ In non-abelian gauge theory: Mohammedi ht/95; Duff IJMPA(96) and IJMPD(96) [in supersymmetric gauge theory, from strings]; Martín MPLA(99) [in path space]; Chan & Tsou IJMPA(99)ht; Tsou ht/00-ln, ht/00-in; Faddeev & Niemi PLB(02)ht/01 [SU(2) Yang-Mills]; Majumdar & Sharatchandra IJMPA(02); Deser & Seminara PLB(05)ht [duality invariance for free bosonic and fermionic gauge fields].
@ Sigma models: Mohammedi et al ZPC(97)ht/95; Mohammedi PLB(96)ht/95, PLB(96).
@ In general relativity: Hawking & Ross PRD(95)ht [electric and magnetic black holes]; Maartens & Bassett CQG(98)gq/97; Nouri-Zonoz et al CQG(99)gq/98 [NUT]; Dadhich MPLA(99)gq/98, MPLA(99), GRG(00)gq/99; Abramo et al MPLA(03) [with scalar field]; Henneaux & Teitelboim PRD(05)gq [linearized gravity]; Deser & Seminara PRD(05)ht [failure in non-linear case]; Julia ht/05-in.
@ Scale factor duality in cosmology: Clancy et al CQG(98)gq; Di Pietro gq/01/MPLA [quintessence].
@ Related topics: Gaona & García IJMPA(07) [first-order actions]; Lindström et al a0707 [T-duality for generalized Kähler geometries].
> Related topics: see gravitomagnetism; self-dual fields [connections] and self-dual solutions in general relativity [Weyl tensor].
> Other dualities: see Galerkin Duality.

Dual Mass in Gravitation
@ General references: Lubkin IJTP(77); Magnon JMP(87), NCA(88); Torre CQG(95)gq/94.
@ Phenomenology: Cates et al GRG(88); Rahvar & Habibi ApJ(04)ap/03 [microlensing signatures]; Danehkar a0707-MPLA.

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